# Theoretical Model: Condorcet's Jury Theorem, Part 1

Theoretical Model: Condorcet's Jury Theorem, Part 1

This is the first of five Demonstrations about Condorcet's jury theorem (1785). It uses the formula , where the probability and is the number of voters. The theorem states if the voters are independent and each has probability of voting for the correct choice, then the probability of the majority voting for the correct choice is larger than and converges to one as the population goes to infinity.

P(N,p)=

×p(1-p)

N

∑

k=⌈N/2⌉

N |

k |

k

N-k

p=0.5+ϵ

N

p=0.5+ϵ>0.5

P(N,p)

p

N